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<div class="titlepage"><div><div><h5 class="title">
<a name="boost_numeric_bindings.reference.lapack.computational_routines.tgsen"></a><a class="link" href="tgsen.html" title="tgsen">tgsen</a>
</h5></div></div></div>
<a name="boost_numeric_bindings.reference.lapack.computational_routines.tgsen.prototype"></a><h6>
<a name="id1067047"></a>
            <a class="link" href="tgsen.html#boost_numeric_bindings.reference.lapack.computational_routines.tgsen.prototype">Prototype</a>
          </h6>
<p>
            There are two prototypes of <code class="computeroutput"><span class="identifier">tgsen</span></code>
            available, please see below. 
</p>
<pre class="programlisting"><span class="identifier">tgsen</span><span class="special">(</span> <span class="keyword">const</span> <span class="identifier">int_t</span> <span class="identifier">ijob</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">fortran_bool_t</span> <span class="identifier">wantq</span><span class="special">,</span>
        <span class="keyword">const</span> <span class="identifier">fortran_bool_t</span> <span class="identifier">wantz</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">VectorSELECT</span><span class="special">&amp;</span> <span class="identifier">select</span><span class="special">,</span> <span class="identifier">MatrixA</span><span class="special">&amp;</span> <span class="identifier">a</span><span class="special">,</span>
        <span class="identifier">MatrixB</span><span class="special">&amp;</span> <span class="identifier">b</span><span class="special">,</span> <span class="identifier">VectorALPHAR</span><span class="special">&amp;</span> <span class="identifier">alphar</span><span class="special">,</span> <span class="identifier">VectorALPHAI</span><span class="special">&amp;</span> <span class="identifier">alphai</span><span class="special">,</span>
        <span class="identifier">VectorBETA</span><span class="special">&amp;</span> <span class="identifier">beta</span><span class="special">,</span> <span class="identifier">MatrixQ</span><span class="special">&amp;</span> <span class="identifier">q</span><span class="special">,</span> <span class="identifier">MatrixZ</span><span class="special">&amp;</span> <span class="identifier">z</span><span class="special">,</span> <span class="identifier">int_t</span><span class="special">&amp;</span> <span class="identifier">m</span><span class="special">,</span>
        <span class="identifier">Scalar</span> <span class="special">&gt;,</span> <span class="identifier">Scalar</span> <span class="special">&gt;,</span> <span class="identifier">VectorDIF</span><span class="special">&amp;</span> <span class="identifier">dif</span> <span class="special">);</span>
</pre>
<p>
          </p>
<p>
            
</p>
<pre class="programlisting"><span class="identifier">tgsen</span><span class="special">(</span> <span class="keyword">const</span> <span class="identifier">int_t</span> <span class="identifier">ijob</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">fortran_bool_t</span> <span class="identifier">wantq</span><span class="special">,</span>
        <span class="keyword">const</span> <span class="identifier">fortran_bool_t</span> <span class="identifier">wantz</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">VectorSELECT</span><span class="special">&amp;</span> <span class="identifier">select</span><span class="special">,</span> <span class="identifier">MatrixA</span><span class="special">&amp;</span> <span class="identifier">a</span><span class="special">,</span>
        <span class="identifier">MatrixB</span><span class="special">&amp;</span> <span class="identifier">b</span><span class="special">,</span> <span class="identifier">VectorALPHA</span><span class="special">&amp;</span> <span class="identifier">alpha</span><span class="special">,</span> <span class="identifier">VectorBETA</span><span class="special">&amp;</span> <span class="identifier">beta</span><span class="special">,</span> <span class="identifier">MatrixQ</span><span class="special">&amp;</span> <span class="identifier">q</span><span class="special">,</span>
        <span class="identifier">MatrixZ</span><span class="special">&amp;</span> <span class="identifier">z</span><span class="special">,</span> <span class="identifier">int_t</span><span class="special">&amp;</span> <span class="identifier">m</span><span class="special">,</span> <span class="identifier">Scalar</span> <span class="special">&gt;,</span> <span class="identifier">Scalar</span> <span class="special">&gt;,</span> <span class="identifier">VectorDIF</span><span class="special">&amp;</span> <span class="identifier">dif</span> <span class="special">);</span>
</pre>
<p>
          </p>
<a name="boost_numeric_bindings.reference.lapack.computational_routines.tgsen.description"></a><h6>
<a name="id1067767"></a>
            <a class="link" href="tgsen.html#boost_numeric_bindings.reference.lapack.computational_routines.tgsen.description">Description</a>
          </h6>
<p>
            <code class="computeroutput"><span class="identifier">tgsen</span></code> (short for $FRIENDLY_NAME)
            provides a C++ interface to LAPACK routines STGSEN, DTGSEN, CTGSEN, and
            ZTGSEN. <code class="computeroutput"><span class="identifier">tgsen</span></code> reorders
            the generalized Schur decomposition of a complex matrix pair (A, B) (in
            terms of an unitary equivalence trans- formation Q' * (A, B) * Z), so
            that a selected cluster of eigenvalues appears in the leading diagonal
            blocks of the pair (A,B). The leading columns of Q and Z form unitary
            bases of the corresponding left and right eigenspaces (deflating subspaces).
            (A, B) must be in generalized Schur canonical form, that is, A and B
            are both upper triangular.
          </p>
<p>
            <code class="computeroutput"><span class="identifier">tgsen</span></code> also computes the
            generalized eigenvalues
          </p>
<p>
            w(j)= ALPHA(j) / BETA(j)
          </p>
<p>
            of the reordered matrix pair (A, B).
          </p>
<p>
            Optionally, the routine computes estimates of reciprocal condition numbers
            for eigenvalues and eigenspaces. These are Difu[(A11,B11), (A22,B22)]
            and Difl[(A11,B11), (A22,B22)], i.e. the separation(s) between the matrix
            pairs (A11, B11) and (A22,B22) that correspond to the selected cluster
            and the eigenvalues outside the cluster, resp., and norms of "projections"
            onto left and right eigenspaces w.r.t. the selected cluster in the (1,1)-block.
          </p>
<p>
            The selection of the LAPACK routine is done during compile-time, and
            is determined by the type of values contained in type <code class="computeroutput"><span class="identifier">VectorSELECT</span></code>.
            The type of values is obtained through the <code class="computeroutput"><span class="identifier">value_type</span></code>
            meta-function <code class="computeroutput"><span class="keyword">typename</span> <span class="identifier">value_type</span><span class="special">&lt;</span><span class="identifier">VectorSELECT</span><span class="special">&gt;::</span><span class="identifier">type</span></code>. The dispatching table below illustrates
            to which specific routine the code path will be generated.
          </p>
<div class="table">
<a name="boost_numeric_bindings.reference.lapack.computational_routines.tgsen.dispatching_of_tgsen"></a><p class="title"><b>Table&#160;1.336.&#160;Dispatching of tgsen</b></p>
<div class="table-contents"><table class="table" summary="Dispatching of tgsen">
<colgroup>
<col>
<col>
</colgroup>
<thead><tr>
<th>
                    <p>
                      Value type of VectorSELECT
                    </p>
                  </th>
<th>
                    <p>
                      LAPACK routine
                    </p>
                  </th>
</tr></thead>
<tbody>
<tr>
<td>
                    <p>
                      <code class="computeroutput"><span class="keyword">float</span></code>
                    </p>
                  </td>
<td>
                    <p>
                      STGSEN
                    </p>
                  </td>
</tr>
<tr>
<td>
                    <p>
                      <code class="computeroutput"><span class="keyword">double</span></code>
                    </p>
                  </td>
<td>
                    <p>
                      DTGSEN
                    </p>
                  </td>
</tr>
<tr>
<td>
                    <p>
                      <code class="computeroutput"><span class="identifier">complex</span><span class="special">&lt;</span><span class="keyword">float</span><span class="special">&gt;</span></code>
                    </p>
                  </td>
<td>
                    <p>
                      CTGSEN
                    </p>
                  </td>
</tr>
<tr>
<td>
                    <p>
                      <code class="computeroutput"><span class="identifier">complex</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;</span></code>
                    </p>
                  </td>
<td>
                    <p>
                      ZTGSEN
                    </p>
                  </td>
</tr>
</tbody>
</table></div>
</div>
<br class="table-break"><a name="boost_numeric_bindings.reference.lapack.computational_routines.tgsen.definition"></a><h6>
<a name="id1068134"></a>
            <a class="link" href="tgsen.html#boost_numeric_bindings.reference.lapack.computational_routines.tgsen.definition">Definition</a>
          </h6>
<p>
            Defined in header <code class="computeroutput">boost/numeric/bindings/lapack/computational/tgsen.hpp</code>.
          </p>
<a name="boost_numeric_bindings.reference.lapack.computational_routines.tgsen.parameters_or_requirements_on_types"></a><h6>
<a name="id1068174"></a>
            <a class="link" href="tgsen.html#boost_numeric_bindings.reference.lapack.computational_routines.tgsen.parameters_or_requirements_on_types">Parameters
            or Requirements on Types</a>
          </h6>
<div class="variablelist">
<p class="title"><b>Parameters</b></p>
<dl>
<dt><span class="term">MatrixA</span></dt>
<dd><p>
                  The definition of term 1
                </p></dd>
<dt><span class="term">MatrixB</span></dt>
<dd><p>
                  The definition of term 2
                </p></dd>
<dt><span class="term">MatrixC</span></dt>
<dd>
<p>
                  The definition of term 3.
                </p>
<p>
                  Definitions may contain paragraphs.
                </p>
</dd>
</dl>
</div>
<a name="boost_numeric_bindings.reference.lapack.computational_routines.tgsen.complexity"></a><h6>
<a name="id1068261"></a>
            <a class="link" href="tgsen.html#boost_numeric_bindings.reference.lapack.computational_routines.tgsen.complexity">Complexity</a>
          </h6>
<a name="boost_numeric_bindings.reference.lapack.computational_routines.tgsen.example"></a><h6>
<a name="id1068288"></a>
            <a class="link" href="tgsen.html#boost_numeric_bindings.reference.lapack.computational_routines.tgsen.example">Example</a>
          </h6>
<p>
            
</p>
<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">numeric</span><span class="special">/</span><span class="identifier">bindings</span><span class="special">/</span><span class="identifier">lapack</span><span class="special">/</span><span class="identifier">computational</span><span class="special">/</span><span class="identifier">tgsen</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
<span class="keyword">using</span> <span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">numeric</span><span class="special">::</span><span class="identifier">bindings</span><span class="special">;</span>

<span class="identifier">lapack</span><span class="special">::</span><span class="identifier">tgsen</span><span class="special">(</span> <span class="identifier">x</span><span class="special">,</span> <span class="identifier">y</span><span class="special">,</span> <span class="identifier">z</span> <span class="special">);</span>

</pre>
<p>
          </p>
<p>
            this will output
          </p>
<p>
            
</p>
<pre class="programlisting"><span class="special">[</span><span class="number">5</span><span class="special">]</span> <span class="number">0</span> <span class="number">1</span> <span class="number">2</span> <span class="number">3</span> <span class="number">4</span> <span class="number">5</span>
</pre>
<p>
          </p>
<a name="boost_numeric_bindings.reference.lapack.computational_routines.tgsen.notes"></a><h6>
<a name="id1068573"></a>
            <a class="link" href="tgsen.html#boost_numeric_bindings.reference.lapack.computational_routines.tgsen.notes">Notes</a>
          </h6>
<a name="boost_numeric_bindings.reference.lapack.computational_routines.tgsen.see_also"></a><h6>
<a name="id1068598"></a>
            <a class="link" href="tgsen.html#boost_numeric_bindings.reference.lapack.computational_routines.tgsen.see_also">See
            Also</a>
          </h6>
<div class="itemizedlist"><ul class="itemizedlist" type="disc"><li class="listitem">
                Originating Fortran source files <a href="http://www.netlib.org/lapack/single/stgsen.f" target="_top">stgsen.f</a>,
                <a href="http://www.netlib.org/lapack/double/dtgsen.f" target="_top">dtgsen.f</a>,
                <a href="http://www.netlib.org/lapack/complex/ctgsen.f" target="_top">ctgsen.f</a>,
                and <a href="http://www.netlib.org/lapack/complex16/ztgsen.f" target="_top">ztgsen.f</a>
                at Netlib.
              </li></ul></div>
</div>
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
<td align="left"></td>
<td align="right"><div class="copyright-footer">Copyright &#169; 2002 -2009 Rutger ter Borg, Kre&#353;imir Fresl, Thomas Klimpel,
      Toon Knapen, Karl Meerbergen<p>
        Distributed under the Boost Software License, Version 1.0. (See accompanying
        file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
      </p>
</div></td>
</tr></table>
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